I appreciated and enjoyed your very concise yet lucid essay. I agree with you that as of its present state, mathematics is unable to represent the concepts you mentioned, but I also believe that at present we have barely touched the expressive power of mathematics.
The limitations you point out in your essay are, I believe, ultimately due to the fact that classical logic permits only a binary distinction between true and false propositions. However, there are many, many other kinds of logic, and who is to say that one cannot construct mathematical systems on these which can, if not completely represent the things you mentioned, cone much closer to doing so? The lowest hanging fruit among them is, in my opinion, existence, and in my own entry I argue that extending classical logic by two non-classical ones permits us to define modes of existence which can be mapped to a possible distinction that exists in the real world at microscopic scales. Note, this sort of endeavor is still, as far as I can tell, in its infancy, so even if it does not overcome some the limitations as you point them out, it is not necessarily the case, in my opinion, that it never will.
Nevertheless, I agree that it is a good idea to keep in the back of one's mind the limitations of mathematical representation, if only to try to break through them.